Ball on String, Calc V with mass, answer by "accident?"

Hi all, concerned Dad here - looking for a validating opinion on the following and would be eternally grateful with some guidance/help. The attachment, Unit4ExamAQ7c is from one of my son's honor's exams. He gets #7c CORRECT with the answer v=2.29 m/s. However, the teacher grades him WRONG as he claims the answer was achieved "by accident." I asked an engineer friend to review the answer and his response was "the grader got it wrong due to laziness." his response is in the attachment ReviewofPhysicsExams. Thank you VERY much!!

Staff: Mentor

Where did the angle get introduced? In the way it is used, it is apparently between the string and the vertical, but you should never make others guess that.
The formula works, but where does it come from? Certainly not from the wrong ##F_T = \frac{mv}r^2## to the left of it (and you need the correct version of it to arrive at the formula with the speed). If it was provided somewhere else on the page, things might be different.

Where did the angle get introduced? In the way it is used, it is apparently between the string and the vertical, but you should never make others guess that.
The formula works, but where does it come from? Certainly not from the wrong ##F_T = \frac{mv}r^2## to the left of it (and you need the correct version of it to arrive at the formula with the speed). If it was provided somewhere else on the page, things might be different.

The formula is provided at the top of the page - I mistakenly cut it off. the new attachment contains Question 7 with the formula.

and therefore, The angle θ ("theta") is in introduced by the formula provided on the exam. Its true that it would've been more clear to have labeled it on the diagram, but he used it correctly regardless, and got the correct answer.

Because of the fact that the formula was provided at the top of the page, you could argue that the onus was on the writer of the test to label θ on the diagram, and that the common convention of θ being the angle between the string and the vertical was already implied in the context of the problem.

Staff: Mentor

It is strange to have such a specific formula there, but if it is given, then I don't see why you shouldn't use it.

Apparently he did use it: The question remains, why would the teacher claim that the correct answer was achieved "by accident?" This is still what I need to determine as the teacher seems to be simply wrong - and, I need credible help to prove it.

Apparently he did use it: The question remains, why would the teacher claim that the correct answer was achieved "by accident?" This is still what I need to determine as the teacher seems to be simply wrong - and, I need credible help to prove it.

Staff: Mentor

You can edit your posts if you want to add something.

I'm not that teacher, and I cannot read his mind. Speaking with him is the only option to influence the grade in any way. I would point out that the formula used was given at the top of the page, and applies to the problem with the proper definition of theta, and apparently was included in the list with this problem in mind, because it fits directly to it. And your son figured out where theta has to be = which quantity goes into numerator and denominator.

I think the formula was intended for the problem of a car on a banked, frictionless road. You happen to get the same formula for this problem, but the teacher probably didn't realize the coincidence and expected students to derive it for this problem.

I'm not that teacher, and I cannot read his mind. Speaking with him is the only option to influence the grade in any way. I would point out that the formula used was given at the top of the page, and applies to the problem with the proper definition of theta, and apparently was included in the list with this problem in mind, because it fits directly to it. And your son figured out where theta has to be = which quantity goes into numerator and denominator.

So, let me ask you a straightforward question, is the problem solved correctly/validly?

I am forever complaining to students posting on these forums that a quoted equation means nothing until you specify the context and what the variables represent in that context. Here we have an examination paper committing the same solecism.
A student taking the paper might happen to remember a formula that applies to the given question, from past experience. Seeing the identical formula in a list provided in the exam, but without context, the student would reasonably assume it was intended to be used for this question. I have no hesitation in declaring that the exam setter created the difficulty and should give the student the benefit of the doubt.
In future, the exam setter should provide context for each standard equation listed; or, at least, provide a separate list per question.